1. Fachtagung TestRig - Juni 2022 27 Evaluation of an Electrodynamic 3D-shaker System using different MIMO Vibration Controllers Kurthan Kersch Robert Bosch GmbH, Powertrain Solutions, Center of Competence for Vibration, 71701 Schwieberdingen, Germany Christian Dindorf Robert Bosch GmbH, Powertrain Solutions, Center of Competence for Vibration, 71701 Schwieberdingen, Germany Thomas Kuttner Bundeswehr University Munich, Faculty of Mechanical Engineering, 85577 Neubiberg, Germany Elmar Woschke Otto von Guericke University Magdeburg, IFME Institute of Mechanics, 39106 Magdeburg, Germany Abstract Multi-axis vibration testing has become known as more realistic than commonly performed uniaxial tests. Failure modes can be reproduced in a more realistic manner. Furthermore, the fatigue damage caused by simultaneous excitation of all axes can be higher than performing sequential uniaxial tests. In order to perform multi-axis vibration testing for automotive components, Bosch has conducted several investigations on an electrodynamic 3D-shaker. The system is manufactured by IMV corporation and contains five shakers to obtain a rated force of 30 kN for each axis. As a preliminary step, the previous evaluation of the electrodynamic shaker system is extended. Therefore, further constraints of the fixture modifications are introduced and applied to an optimum test setup for larger and broader components. Then, a qualitative qualification test is conducted with a full multiaxial profile including amplitudes, phases and coherences. As an emphasis of the analysis, different controlling systems are used for the investigation. Thereby, also a quantitative comparison of the different controllers is made with respect to accuracy and functionality. During the studies, several assessment criteria for multi axis controllers are developed. 1. Introduction Vibration testing is an important step for the validation of newly developed automotive parts and structures. Test profiles are usually derived with different driving scenarios to cover all possible load situations. Within the automotive industry, vibration testing is mainly conducted on uniaxial shakers on which all relevant industrial standards are based. Gradually, the need to perform more multi-axis testing, resulting in a more realistic reproduction of the field loads, has arisen among the respective manufacturers. On contrary to aerospace applications, multi-axis testing is not established within the automotive industry which results in a lack of respective standards and methods. One of the main reasons are partially higher acceleration levels and frequency ranges up to 2000 Hz that are typically required within the scope of automotive testing, as can be seen in [5]. Multiaxial shaker systems with the respective requirements are no widely available standard equipment. The systems used in literature are mostly prototypes which serve for a scientific purpose. Both implementation and handling of the system is thereby usually described sparely. The main challenge of multi-axis shakers is the construction and handling of the bearing unit which couples the different shaker axes. For large industrial shakers, such as needed for automotive testing, resonances of the bearing unit due to the low stiffness are unavoidable which may violate the results, as indicated in [3]. A six-degree-of-freedom shaker is investigated [10], where both occurring system resonances are left unconsidered during testing. The shaker system evaluated in this work was previously investigated in [8], showing a complex, non-linear behavior with roughly 14 modes within a frequency range of 10 to 2000 Hz. As conclusion, for every shaker model a qualification test has to be undertaken. In this work, the main points of the preliminary investigations in [8] are recapitulated and complemented with further requirements of the manufacturer considering the fixture modification. 28 1. Fachtagung TestRig - Juni 2022 Evaluation of an Electrodynamic 3D-shaker System using different MIMO Vibration Controllers A new test setup for larger components is shown and a qualitative qualification test is undertaken. As a next step, the influence of two different vibration control systems are evaluated. Thereby, measurable assessment criteria are defined and applied to the respective shaker system. 2. Shaker Evaluation 2.1 System Description Subject of this work is an electrodynamic 3D-shaker system prototype which is shown in fig. 1 and labeled as IMV TS-3000-3.2H-CE. It consists of five independent shakers which are coupled through a bearing unit, as illustrated in fig. 2. Both horizontal axes (X and Y) are excited with two 15 kN shakers each, which are arranged in a push-pull configuration. The vertical Z-axis contains a single 30 kN shaker. Due to its quadratic design with an edge length of 320 mm and a number of 25 threaded holes, the usage of the shaker table is limited regarding the test setup. Figure 1: 3D-shaker system [8] Figure 2: Illustration of the 3D-shaker setup [6] In order to balance the systems bearing unit, a counterweight is mounted at its bottom as shown in fig. 2. Especially rotational modes around the horizontal axes, usually occurring at the vicinity of 110 Hz, may produce displacements that cause damage to the bearing unit. A respective specification for the balancing is provided in [4]. It contains upper and lower limits for the pairing of mass and height of the Center of Gravity (CoG), as indicated in fig. 3 which have to be maintained for extensive and endurance testing. Figure 3: Specification for shaker setup [6] In the preceding investigation [8], a preliminary sine sweep of the 3D-shaker with a bare setup showed roughly 14 resonances in total within a frequency range of 10 Hz to 2000 Hz. Some modes occur as harmonics or do only develop with a simultaneous XYZ-excitation indicating a nonlinear behavior. A more detailed description of the modes can be found in [6], based on Operational Deflection Shape (ODS) analyses. However, a shaker characterization in terms of Experimental Modal Analysis (EMA) turned out to be not meaningful due to the high system complexity. 2.2 Fixture Modification As a next step, different geometries were used in [8] as a modification to perform optimum measurements up to 2000 Hz. They are shown in fig. 4 and do mostly not comply with the specifications given in fig. 3, except the setup with a block and two frames (given in fig. 5). This setup, where the specimens are to be mounted and controlled on the top of the block, was also determined to be the optimum for small, central mounted and single-point controlled structures. The particular reasons are increased response signals due to the raised position and an increased stiffness which shifts a critical mode around 1850 Hz into a higher frequency range while lowering its modal participation. The two frames are applied in order to meet the required boundaries of fig. 3 and further enhance the setup by further increased stiffness. The entire setup has a total mass of 13.3 kg and a CoG height of 46 mm. 1. Fachtagung TestRig - Juni 2022 29 Evaluation of an Electrodynamic 3D-shaker System using different MIMO Vibration Controllers Figure 4: Different fixture setups for the evaluation [8] Figure 5: Setup for control location at center The control point is generally chosen to be close to the mounting locations of the specimen since the response power at any arbitrary point on the structure usually deviates from the responses at the control location. For larger or broader components, the given setup, as well as the central control position cannot be used anymore. Therefore, another setup has to be developed where a meaningful control can be accomplished at a more peripheral location. A plane structure is manufactured from a solid block shown in fig. 6 and referred to as adapter plate. Cavities are inserted at the bottom to meet the required mass (13.5 kg) and CoG height (45 mm), as shown in fig. 7. While the center of the adapter plate is not appropriate as control location for the critical mode around 1850 Hz, the setup can be controlled near the edge, as can be seen in fig. 6. Figure 6: Setup for control location at the edge [6] Figure 7: Setup for control location at the edge, bottom view [6] In a next step, the adapter plate is used for a real testing scenario. A typical fixture of a complex automotive component is mounted on the adapter plate, as shown in fig. 8 with the control location M1. The fixture enables the mounting of two components at the same time, however, only one is used for the test. Due to security of corporate know-how, the component is not shown in the figure. The entire test setup has a total weight of 18.3 kg and a total CoG height of around 50 mm and is thus compliant with the specifications in fig. 3. Figure 8: Setup for complex automotive component (not shown in picture, two units can be mounted) [6] 30 1. Fachtagung TestRig - Juni 2022 Evaluation of an Electrodynamic 3D-shaker System using different MIMO Vibration Controllers The random vibration test profile (critical frequency range of 10-1700 Hz) is derived from two vehicle measurements according to the method described in [7]. It is given in fig. 9 with the PSD values on the diagonals, the phases on the upper triangle and the magnitude squared coherences on the lower triangle. As vibration controller, the Dataphysics Signal Star Matrix was used for the test. The measurements are performed with triaxial Dytran 3133 series accelerometers and the control is performed with a triaxial PCB 356A61 accelerometer. The qualitative comparison between the defined profile and the actual measurements concludes in an accurate replication of the desired test definition. Figure 9: Profile (in red) and measured test values (in blue) for a complex automotive component, phases on the upper triangle, magnitude squared coherences on the lower triangle [6] 3. Vibration Controller Evaluation Apart from the 3D-shaker system itself, the vibration controller is of crucial importance, especially regarding its software component. In this section, different controllers and their particular configuration are compared qualitatively with measurable criteria that are to be defined beforehand. Since no insight into the controller programming is possible, it is treated as a black box. Vibration control actions are especially needed around resonances. The drive signals are decreased respectively to avoid overshoots or increased when being located at a vibrational node. Difficulties may occur if the resulting cross accelerations due to mass inertia counter the target profile, as can be seen exemplary in [3]. Furthermore, nonlinear behavior such as amplitude sensitive FRFs or unsteady vibrational nodes may lead to overshoots of the defined profile. In a complex system several issues may also occur at the same time. From a control perspective, a forced phase response (phase control) may also lead to distortions of the defined profiles. 3.1 Definition of Measurable Evaluation Criteria At first, measurable criteria are to be defined for the comparison since no differences in the front-ends of the considered controllers are observable. Therefore, the flowchart for random vibration control in fig. 10 according to [9] is referred and marked respectively. The control reference for random vibration is a positive definite Spectral Density Matrix (SDM). The aim of the entire process is to match the output spectrum with the reference. The predicted output Fourier spectrum is calculated based on a random part, a reference part and the system transfer matrix. They can be characterized as decoupled inputs. The random part is a vector of independent noise sources that are realized with a randomization of the phases and is also known as pseudo random. A Cholesky decomposition of the reference spectrum is used to obtain the reference part. Depending on the SDM, the decoupled inputs can be fully, partly or not correlated. The core of the control action is the algorithm that updates the decoupled inputs. Two basic approaches exist: The update of the reference part and updating the transfer matrix. The first approach numerically finds an update for both amplitude and phase based on the error, the second one continuously recalculates the transfer matrix. Both approaches can also be used together. The first defined criterion is the system identification process. It gives evidence about the processing of the initial transfer matrix and thus the starting point of the control actions. The accuracy of the system identification can be influenced by the type of random signal generation that is used. Apart from the already mentioned pseudo random, the so-called pure random is oftenly used. It is basically a random number generator based signal, as described in [2]. The different effects on the system identification are explained in [1], stating that better estimates of the frequency response functions can be achieved using pseudo random. Since the drive spectra being usually described in terms of voltage, the transfer matrix is given in terms of [(m/ s²)/ V]. The second criterion is the stability of the control loop in presence of disturbances as for example hum noise (current noise) that occurs on the amplifiers, as already described in [8]. The third detected criterion concerns the configuration of the control process algorithm. As mentioned beforehand, two basic methods are available: Updating the inputs through an error correction and updating the full transfer matrix. Figure 10: Flow-chart of random vibration control algorithm with measurable criteria for controller comparison 1. Fachtagung TestRig - Juni 2022 31 Evaluation of an Electrodynamic 3D-shaker System using different MIMO Vibration Controllers 3.2 Comparison of Different Systems A qualitative comparison of the respective profile conformity is used to evaluate the differences. Two controllers are considered for the analysis. For all tests, the exactly same adjustable parameters are used for signal processing (PSD calculation), control steps (frequency lines and bandwidth) and initial input voltage (used for system identification). The transfer functions of the initial system identifications are shown in fig. 11 for both controllers and using a bare table setup. They show moderate deviations on the main axes and larger deviations on its cross-axes, especially in the higher frequency range. The most obvious reason appears to be the difference in the initial excitation: While controller 1 performs a continuous excitation, controller 2 conducts the initial excitation batch-wise. Thereby, the excited resonances are likely to fade while in the first case modes are able to develop. Furthermore, a cause might be the strongly nonlinear behavior of the shaker. Figure 11: Initial transfer functions of controller 1 (red) and controller 2 (black) [6] The next criterion, which is the influence of disturbances on the control loop stability, is evaluated with the setup from fig. 5. A low-level white noise random excitation is applied. The resulting PSD responses, which are given in fig. 12, show that controller 2 is able to remove the hum noise that is especially present at 850 Hz and 950 Hz. The reason for the difference might be a band stop filter, respectively a notch filter that removes hum noise at every 50 Hz in European power networks (60 Hz in US and parts of Asia). A notch filter is a strongly narrow version of a band pass filter which allows the reduction of noise without strong influence on the desired transfer functions. The results of the initial system identification, previously given in fig. 11, also show hardly any noise using controller 2. Figure 12: Influence of current noise at 850 Hz and 950 Hz on controller 1 and 2 [6] The configuration of the control process is evaluated with the same test setup that was used previously. While no difference can be detected for a standard continuous random vibration test, major advantages of using a transfer matrix update are detected for deterministic vibration control. Fig. 13 shows the PSD responses of different Time Waveform Replication (TWR) tests using an example signal. Thereby, the transfer matrix is updated during testing which is referred to as adaptive control, according to [11]. Besides a peak at 1450 Hz due to hum noise, no difference in accuracy is detected between controller 1 and 2 when omitting the adaptive control, which is not provided by controller 1 at all. Figure 13: Time Waveform Replication of an example signal with different controller configurations [6] 4. Conclusion This paper aimed at extending the preceding investigations of an electrodynamic 3D-shaker system. Thereby, further aspects of the fixture modification were introduced. A new fixture for larger components was proposed and evaluated with an example vibration test. An emphasis of the investigation was put on the influence of different vibration controllers. Several assessment criteria were defined and applied using two different vibration controllers. 32 1. Fachtagung TestRig - Juni 2022 Evaluation of an Electrodynamic 3D-shaker System using different MIMO Vibration Controllers The particular investigation concludes in the utility of notch filters, as well as adaptive control for an accurate vibration testing. Furthermore, the precision of the initial system identification may take a positive influence on the vibration control with providing reasonable start values. When conducting a controller analysis, it is beneficial to start with simple conformity comparisons. Thereby, either simple profiles can be used or the excitation of only one axis while keeping both other axes as close to zero as possible (zero-reference control). References [1] Cornelis; Toso; Verpoest; Peeters (2014): Improved MIMO FRF estimation and model updating for robust time waveform replication on durability test rigs. Proc. 26th ISMA including USD, pp. 737-752. [2] Gatto; Peeters; Coppotelli (2010): Flexible shaker excitation signals for improved FRFestimation and non-linearity assessment. Proc. 24th ISMA including USD, pp. 2475-2488. [3] Gregory; Bitsie; Smallwood (2008): Comparison of the response of a simple structure to single axis and multiple axis random vibration inputs. Proc. 79th Shock and Vibration Symposium. [4] IMV Corporation (2015): Operation Manual. [5] International Organization for Standardization (2012): ISO 16750-3: Road Vehicles - Environmental Conditions and Testing for Electrical and Electronic Equipment - Mechanical Loads. [6] Kersch (2020): 3D-Shaker Testing for Automotive Components (PhD Thesis). University of Magdeburg. [7] Kersch; Wagner; Kuttner; Woschke (2020): Improved techniques for uniaxial and multiaxial vibration test profile definition. Journal of the IEST, vol. 63, no. 1. [8] Kersch; Woschke (2020): Fixture modifications for effective control of an electrodynamic 3D-shaker system. Sound and Vibration, vol. 54, no. 2, pp. 75- 84. [9] Peeters; Debille (2002): Multiple-input-multipleoutput random vibration control: Theory and practice. Proc. 20th ISMA, pp. 507-516. [10] Smallwood; Gregory (2008): Evaluation of a six- DOF electrodynamic shaker system. Proc. 79th Shock and Vibration Symposium. [11] Underwood; Ayres; Keller (2011): Filling in the MIMO matrix, part 2 time waveform replication tests using field data. Sound and Vibration, vol. 45, no. 9, pp. 8-17.